In the figure shown a parallel plate capacitor is connected across a source of emf `epsilon`. The plates are square shaped with edge 'l' and separated by a distance d. A dielectric slab of dielectric constant k and thickness d is inserted between the plates with constant speed v. Find the current in the connecting wires, ignore the resistance of connecting wires. A current of equal strength is passed through a coil of resistance R and dipped into water kept in a bucket at `0^(@)C`. What would be the temperature of the water at the end of 5 minutes if mass of the water is m and specific heat of the water is c?

Explanation

Consider that length x of the dielectric is inside the capacitor. The capacitance of the system is
`C=(epsilon_(0)kxl)/(d)+(epsilon_(0)l(l-x))/(d)=(epsilon_(0)l)/(d)[(k-1)x+l]`
Charge on the capacitor
`q=(epsilon_(0)l)/(d)[(k-1)x+l]epsilon`
`implies (dq)/(dt)=(epsilon_(0)l)/(d)(k-1)epsilon(dx)/(dt)`
`implies l=(epsilon_(0)l epsilonv(k-1))/(d)`
`because` Heat produced in time `t = l^(2)Rt`
Let temp. of the water increase by T
`implies mcT=l^(2)Rt`
`T=(l^(2)Rt)/(mc)`